# Supergalactic coordinate system

In astronomy, supergalactic coordinates are coordinates in a spherical coordinate system which was designed to have its equator aligned with the supergalactic plane, a major structure in the local universe formed by the preferential distribution of nearby galaxy clusters (such as the Virgo cluster, the Great Attractor and the Pisces-Perseus supercluster) towards a (two-dimensional) plane. The supergalactic plane was recognized by Gérard de Vaucouleurs in 1953 from the Shapley-Ames Catalog, although a flattened distribution of nebulae had been noted by William Herschel over 200 years earlier. Vera Rubin had also identified the supergalactic plane in the 1950s, but her data remained unpublished.

By convention, supergalactic latitude is usually abbreviated SGB, and supergalactic longitude as SGL, by analogy to b and l conventionally used for galactic coordinates. The zero point for supergalactic longitude is defined by the intersection of this plane with the galactic plane.

## Definition

• The north supergalactic pole (SGB = 90°) lies at galactic coordinates (lz = 47.37°, bz = +6.32°). In the equatorial coordinate system (epoch J2000), this is approximately RA = 18.9h, Dec = +15.7°.
• The zero point (SGB = 0°, SGL = 0°) lies at (lx = 137.37°, bx = 0°). In J2000 equatorial coordinates, this is approximately 2.82h, +59.5°.

So the transformation from a triple of Cartesian supergalactic coordinates to a triple of galactic coordinates is

${\begin{bmatrix}x\\y\\z\end{bmatrix}}_{\text{gal}}={\begin{bmatrix}\cos l_{x}\cos b_{x}&\sin l_{z}\cos b_{z}\sin b_{x}-\sin b_{z}\sin l_{x}\cos b_{x}&\cos l_{z}\cos b_{z}\\\sin l_{x}\cos b_{x}&\sin b_{z}\cos l_{x}\cos b_{x}-\cos l_{z}\cos b_{z}\sin b_{x}&\sin l_{z}\cos b_{z}\\\sin b_{x}&\cos b_{z}\cos b_{x}\sin \left(l_{x}-l_{z}\right)&\sin b_{z}\end{bmatrix}}{\begin{bmatrix}x\\y\\z\end{bmatrix}}_{\text{superg}}$

The left column in this matrix is the image of the origin of the supergalactic system in the galactic system, the right column in this matrix is the image of the north pole of the supergalactic coordinates in the galactic system, and the middle column is the cross product (to complete the right handed coordinate system).